Solve [[[[v]^[2]] 7v^6]/[4[[v]^[2]] 40v 96]]

Question

Simplify the expression

\frac{7 v ^{5}}{15360}

Evaluate

(\frac{( v ^{2} ) \times 7 v ^{6}}{4 ( v ^{2} ) \times 40 v \times 96})

Remove the parentheses

\frac{( v ^{2} ) \times 7 v ^{6}}{4 ( v ^{2} ) \times 40 v \times 96}

Dividing by a^{n} is the same as multiplying by a^{- n}

\frac{( v ^{2} ) \times 7 v ^{6} \times v ^{- 1}}{4 ( v ^{2} ) \times 40 \times 96}

Calculate

\frac{v ^{2} \times 7 v ^{6} \times v ^{- 1}}{4 ( v ^{2} ) \times 40 \times 96}

Calculate

\frac{v ^{2} \times 7 v ^{6} \times v ^{- 1}}{4 v ^{2} \times 40 \times 96}

Dividing by a^{n} is the same as multiplying by a^{- n}

\frac{v ^{2} \times 7 v ^{6} \times v ^{- 1} \times v ^{- 2}}{4 \times 40 \times 96}

Multiply

More Steps

Multiply the terms

v^{2} \times 7 v^{6} \times v^{- 1} \times v^{- 2}

Multiply the terms with the same base by adding their exponents

v^{2 + 6 - 1 - 2} \times 7

Calculate the sum or difference

v^{5} \times 7

Use the commutative property to reorder the terms

7 v^{5}

\frac{7 v ^{5}}{4 \times 40 \times 96}

Solution

More Steps

Multiply the terms

4 \times 40 \times 96

Multiply the terms

160 \times 96

Multiply the numbers

15360

\frac{7 v ^{5}}{15360}

Show Solution

Find the excluded values

v = 0

Evaluate

(\frac{( v ^{2} ) \times 7 v ^{6}}{4 ( v ^{2} ) \times 40 v \times 96})

To find the excluded values,set the denominators equal to 0

(v^{2}) v = 0

Simplify

More Steps

Evaluate

(v^{2}) v

Calculate

v^{2} \times v

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

v^{2 + 1}

Add the numbers

v^{3}

v^{3} = 0

Solution

v = 0

Show Solution

Find the roots

v \in \emptyset

Evaluate

(\frac{( v ^{2} ) \times 7 v ^{6}}{4 ( v ^{2} ) \times 40 v \times 96})

To find the roots of the expression,set the expression equal to 0

\frac{( v ^{2} ) \times 7 v ^{6}}{4 ( v ^{2} ) \times 40 v \times 96} = 0

Find the domain

More Steps

Evaluate

(v^{2}) v \neq = 0

Simplify

More Steps

Evaluate

(v^{2}) v

Calculate

v^{2} \times v

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

v^{2 + 1}

Add the numbers

v^{3}

v^{3} \neq = 0

The only way a power can not be 0 is when the base not equals 0

v \neq = 0

\frac{( v ^{2} ) \times 7 v ^{6}}{4 ( v ^{2} ) \times 40 v \times 96} = 0, v \neq = 0

Calculate

\frac{( v ^{2} ) \times 7 v ^{6}}{4 ( v ^{2} ) \times 40 v \times 96} = 0

Calculate

\frac{v ^{2} \times 7 v ^{6}}{4 ( v ^{2} ) \times 40 v \times 96} = 0

Calculate

\frac{v ^{2} \times 7 v ^{6}}{4 v ^{2} \times 40 v \times 96} = 0

Multiply

More Steps

Multiply the terms

v^{2} \times 7 v^{6}

Multiply the terms with the same base by adding their exponents

v^{2 + 6} \times 7

Add the numbers

v^{8} \times 7

Use the commutative property to reorder the terms

7 v^{8}

\frac{7 v ^{8}}{4 v ^{2} \times 40 v \times 96} = 0

Multiply

More Steps

Multiply the terms

4 v^{2} \times 40 v \times 96

Multiply the terms

More Steps

Evaluate

4 \times 40 \times 96

Multiply the terms

160 \times 96

Multiply the numbers

15360

15360 v^{2} \times v

Multiply the terms with the same base by adding their exponents

15360 v^{2 + 1}

Add the numbers

15360 v^{3}

\frac{7 v ^{8}}{15360 v ^{3}} = 0

Divide the terms

More Steps

Evaluate

\frac{7 v ^{8}}{15360 v ^{3}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{7 v ^{8 - 3}}{15360}

Reduce the fraction

\frac{7 v ^{5}}{15360}

\frac{7 v ^{5}}{15360} = 0

Simplify

7 v^{5} = 0

Rewrite the expression

v^{5} = 0

The only way a power can be 0 is when the base equals 0

v = 0

Check if the solution is in the defined range

v = 0, v \neq = 0

Solution

v \in \emptyset

Show Solution